Snowball Problem: Differential Equation of Translational Motion

[sheelbe999]

Homework Statement

"A snowball, initially of mass m, slides down a slope inclined at an angle φ with
respect to the horizontal. As it moves, the mass of additional snow Δm = αx that it
accumulates is proportional to the distance traveled x. Write the differential equation
of translational motion for the snowball, ignoring rotation and friction. [6]"

I was sure mass was irrelevant in this situation? But judging by the question its not. Could anyone help me out?

Homework Equations

The Attempt at a Solution

 

[gabbagabbahey]

As always, I'd begin by drawing a picture; what Force(s) act on the snowball, and which direction do they point?

 

[jacsamell]

F=d(mv)/dt
F=v dm/dt + m dv/dt

m=m+ax
dm/dt=av

F=mg sin(*)

mg sin(*)=m dv/dt + a v^2